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" Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Σελίδα 94
των Rev. John Allen - 1822 - 494 σελίδες
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 σελίδες
...opposite angles, &c. Q. E, D. ^ PROP. XXIII. THEOR. Book in. UPON the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with each other. If it be possible, let the two similar segments of circles, ACB, ADB be upon the same side of the same...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 σελίδες
...angles, Sec. QE I). *— y~* PROP. XXIII. THEOR. UPON the same straight line, and upon the same See N. side of it, there cannot be two similar segments of circles not coinciding with one another. If it be possible, let the two similar segments of circles, viz. ACB, ADB, be upon the...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 σελίδες
...opposite angles, &c. QED PROP. XXIII. THEOR. UPON the same straight line, and upon the same See Noteside of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible, let the two similar segments of circles, viz. ACB, ABD be upon the...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813
...circle, are together equal to two right angles. Prop. XXIII. Theor. Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. Prop. XXIV. Tlieor. Similar segments of circles Upon equal straight lines, are equal to...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 σελίδες
...angles. Therefore the opposite angles, &c. QED PROP. XXIII. THEOR. Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible, let the two similar segments of circles, vie. ACB, ADB, be upon the...

The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821
...absurd. C'or. Hence every equiangular triangle is equilateral ; vide, Elrington. PROP. 7. THEOR. i On the same right line and on the same side of it there cannot be two triangles formed whose conterminous sides are equal. If it be possible that there can, 1st, let the...

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 σελίδες
...Therefore, the opposite angles, &c. QED Propotition XXIll. Theorem. Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible, let the two similar segments of circles, viz. ACB, ADB, be upon the...

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 σελίδες
...Therefore, the ppposite angles, &c. QED PROP. XXIII. THEOR. (See N. Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding 'with one another. If it be possible, upon the same straight line AB, and upon the same side of it, let there...

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1829 - 516 σελίδες
...angles. Therefore the opposite angles, &c. QED PROP. XXIII. THEOR. UPON the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another.* Ifitbe possible,letthe two similarsegments of circles, viz. ACB, ABD be upon the same...

The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833
...whole, which is absurd. Cor. Hence every equiangular triangle is equilateral ; vide Elrington. PROP. 7, THEOR. On the same right line and on the same side of it, there cannot be two triangles formed whose conterminous sides are equal. If it be possible that there can, 1st. let the...




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